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34 articles for “Finite Fields”
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Algebraic Foundations of AES (Advanced Encryption Standard): Group Theory and Finite Field Applications in Symmetric Cryptography
Abstract: This paper presents a mathematical study of symmetric cryptographic algorithms, with a particular emphasis on the Advanced Encryption Standard (AES), which is one of the most widely used encryption schemes in modern security applications. The study highlights how abstract mathematical frameworks such as group theory, finite fields, and vector space concepts provide the foundation for the design, implementation, and analysis of AES. By approaching the algorithm from a mathematical perspective, …
Published in Recent Trends in Mathematics · Vol. 2, Issue 1, 2025 · pp. 12–16 Read article
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Revolutionizing Optical Fibre Field Distribution with Linear Finite Element Method
Abstract: This study investigates the use of the linear Finite Element Method (FEM) for the analysis of the field distribution in optical fibres. Understanding the distribution of electric and magnetic fields is necessary to characterise fibre properties including mode profiles, propagation constants, and dispersion, all of which are essential for optimising fibre performance in a range of applications like sensing and telecommunications. This study emphasises on applying a linear FEM formulation …
Published in Trends in Opto-electro & Optical Communication · Vol. 15, Issue 3, 2025 · pp. 32–42 Read article
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Study of Algebraic Structures in Discrete Mathematics and Its Applications
Abstract: Algebraic structures such as groups, rings, fields, semi groups, and lattices form the foundational framework of discrete mathematics. These structures are defined by specific sets and operations that follow algebraic laws, enabling a systematic approach to problem-solving in various domains. This paper explores the theoretical principles of these algebraic systems and highlights their vital role in computer science, cryptography, automata theory, coding theory, and software engineering. By examining their properties …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 35–40 Read article
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Analysis of Field Distribution in Optical Fibre Using FEM Method
Abstract: The application of the linear Finite Element Method (FEM) to the analysis of the field distribution in optical fibres is examined in this work. Characterizing fibre characteristics like mode profiles, propagation constants, and dispersion, all of which are critical for maximizing fibre performance in a variety of applications like sensing and telecommunications, requires an understanding of the distribution of electric and magnetic fields. In order to accurately determine the modal …
Published in Trends in Opto-electro & Optical Communication · Vol. 15, Issue 2, 2025 · pp. 31–40 Read article
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Comprehensive study of Entanglement Entropy in Quantum Field Theory: Analysis of Conformal Field Theory to Massive Field Extensions and Holographic Entanglement
Abstract: This paper provides an in-depth analysis of entanglement entropy (EE) in quantum field theory (QFT), with a particular focus on its computation using the replica trick and its applications to both conformal and non-conformal systems. Beginning with an introduction to the basics of QFT, the study explains how entanglement entropy quantifies the quantum correlations between subsystems in a pure state, represented by the von Neumann entropy of the reduced density …
Published in Research & Reviews : Journal of Physics · Vol. 13, Issue 3, 2024 · pp. 33–58 Read article
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Group-Theoretic Symmetry Indices for Modular Building Layouts under Seismic Load Redistribution
Abstract: Symmetry in modular buildings operates simultaneously as an architectural language, a structural regularizer, and a computational design variable. This paper develops a group-theoretic framework for evaluating and optimizing plan symmetry in modular buildings subjected to seismic load redistribution. The building layout is modeled as a finite occupancy–stiffness field defined on a rectangular lattice, where each module encodes both mass and stiffness contributions. Planar reflections and quarter-turn rotations are represented as …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 01–07 Read article
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An Integrated Simulation Framework for Predicting Dielectric Breakdown and Electrical Aging in Epoxy-Silica Composite Insulation Systems
Abstract: This paper provides a combined computation approach in forecasting the dielectric breakdown and electrical aging within epoxy-silica composite of insulation system. The approach will consist of a three-complementary methodology (a combination of computing electric field using the finite element analysis, estimation of the probability of failures or breakdowns using Weibull statistics, and prediction of degradation tendencies using artificial neural networks). The epoxy-silica composites are of 10-40 volumes fillers. The simulations …
Published in Journal of Polymer & Composites · Vol. 14, Issue 2, 2026 · pp. 339–376 Read article
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Winding Modification and Analysis of LVDT
Abstract: The LVDT (Linear Variable Differential Transformer) typically uses step-winding mode because it has an advantage such as simple construction and fewer layers of winding. The LVDT converts a location or linear movement from a reference standard (zero or null point) impulse with direction and distance information into a proportionate electrical field using the phase and amplitude components. To produce the output in full stroke, the core’s length must be more …
Published in International Journal of Solid State Innovations & Research · Vol. 2, Issue 2, 2024 · pp. 29–35 Read article
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Hybrid Composite Behavior of Concrete-Filled Steel Tube (CFST) Columns: Review of Collapse Mechanisms and Polymer-Based Enhancements
Abstract: Concrete-Filled Steel Tube (CFST) columns are an advanced hybrid composite system where the steel tube's confinement and the concrete core's load capacity work together to improve structural performance. While commonly used in civil engineering, CFSTs can also be understood within the framework of composite materials, similar to polymer- and fiber-reinforced composites, in which interactions between phases determine strength, ductility, and failure modes. This review compiles experimental and numerical research on …
Published in Journal of Polymer & Composites · Vol. 14, Issue 1, 2026 · pp. 78–97 Read article
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Study on the Method of Constructing a System of Linear Equations for Calculating Aerodynamic Derivatives
Abstract: The aerodynamic derivatives can be calculated from the unsteady hydrodynamic forces experienced by the harmonic-oscillating vehicle. Until now, unsteady flow field analysis in aerodynamic derivative calculations has been applied mainly to thin bodies based on potential theory MSC. Nastran is a typical application based on potential theory MSC. Natran can calculate the aerodynamic derivatives of the vehicle relatively well in the subsonic region, but in the supersonic region, the fuselage …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 3, 2025 · pp. 14–24 Read article
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A Shear Strength Reduction Method for an Open Pit Slope Stability Analysis Based on Finite Element Method
Abstract: Slope stability assessment of open pit mines is critically important, since it forms part of the overall productivity and safety management strategy of the mines. The aim of this work is to investigate the overall stability conditions of three (3) open pits in Gold Fields Limited, Tarkwa Ghana. Field and laboratory investigations were conducted as well as empirical methods. Finite Element Analysis (FEA) in Rocscience was carried out using the …
Published in Journal of Geotechnical Engineering · Vol. 13, Issue 1, 2026 · pp. 1–24 Read article
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Chemical Reactor Design and Analysis: A Review
Abstract: Chemical reactors play a critical role in industries such as oil and gas, chemical processing, and power generation, where they operate under extreme pressure and handle highly toxic, compressible fluids. The growing need for alternative energy sources has led to an increased demand for vessels capable of withstanding high pressure and temperature, especially in the chemical and petroleum industries. Recent innovations in chemical reactor technology have concentrated on creating new …
Published in Recent Trends in Fluid Mechanics · Vol. 12, Issue 2, 2025 · pp. 49–59 Read article
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POLYMER AND COMPOSITE-BASED GEOSYNTHETIC REINFORCEMENTS FOR SEISMIC STABILITY OF SOIL RETAINING STRUCTURES: MATERIALS, MECHANICS, AND PERFORMANCE REVIEW
Abstract: Geosynthetic materials based on polymer and composites have become important items for the structural performance and seismic resilience of the reinforced soil retaining systems. Mechanically stabilized earth walls in recent geotechnical engineering practice are increasingly based on enhanced polymeric reinforcements for enhanced tensile strength, durability, flexibility, and energy dissipation under dynamic loading. High-density polyethylene, polypropylene, polyester, and fiber-reinforced polymer composites are usually used. The present review focus on the recent …
Published in Journal of Polymer & Composites · Vol. 14, Issue 4, 2026 Read article
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Numerical Solution of Ordinary Differential Equation and Solution of Partial Differential Equation
Abstract: This research paper explores the fundamental role of various mathematical concepts in engineering and scientific fields like aerospace engineering, materials science, software development, and the energy sector. We delve into the applications of solving algebraic and transcendental equations, finite difference interpolation, numerical methods, solutions to ordinary differential equations (ODEs), and numerical solutions to partial differential equations (PDEs). By examining their applications in these diverse fields, we illustrate the critical importance …
Published in Journal of Aerospace Engineering & Technology · Vol. 14, Issue 3, 2024 · pp. 12–20 Read article
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Numerical Investigation on Concrete Filled Steel Tube Composite Circular Columns Under General Loading
Abstract: Concrete-filled steel tube (CFST) composite columns are extensively utilized in civil engineering constructions because of their numerous structural advantages, such as superior seismic performance, high load- bearing capacity, fire resistance, remarkable ductility, and ability to absorb energy effectively, especially in areas prone to seismic activity. CFST columns are employed in tall buildings and bridges to enhance rigidity and increase bearing capacity, but their behavior can be affected by buckling. There …
Published in Journal of Polymer & Composites · Vol. 13, Issue 2, 2025 · pp. 164–199 Read article
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A Machine Learning-based Analysis of Climate Change
Abstract: Climatic variations are a pressing global challenge that demands immediate and comprehensive attention. A wealth of articles has been published on climate change mitigation and adaptation, yet there remains a need for innovative methods to explore the complexities of climatic variations and to devise more efficient and effective strategies for adjustment and alleviation. With technological advancements, machine learning (ML) and deep learning (DL) approaches have derived significant popularity across various …
Published in Research & Reviews : Journal of Space Science & Technology · Vol. 13, Issue 2, 2024 · pp. 1–10 Read article
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Design And Fabrication of Contactless Magnetic Gears
Abstract: Modern engineering prioritizes speed, efficiency, and reliability, spurring innovations like contactless magnetic gear systems that transmit torque through interacting magnetic fields from permanent magnets, eliminating physical contact to drastically cut friction, backlash, wear, lubrication needs, and heat—operating silently with minimal vibration and peak efficiencies up to 99% under ideal conditions, outperforming traditional gears in low-speed, high-torque direct-drive applications such as motors. The design centers on two rotors: an outer high-speed …
Published in Trends in Mechanical Engineering & Technology · Vol. 16, Issue 2, 2026 Read article
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A Method of Mesh Deformation for Flow Analysis Around Oscillating Bodies
Abstract: In general, high-speed rotating machines are subjected to complex phenomena due to various reasons, such as increased noise and strong vibration due to dynamic unbalance, which affect the dynamic motion of rotating machines and are necessarily a problem to overcome. Therefore, it is necessary to have a mathematical model to simulate it, and a strong tool to solve the constructed model. Using fluid-structure coupling techniques, which are currently a powerful …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 2, 2025 · pp. 35–42 Read article
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Numerical Investigation of Heat Transfer Enhancement in Micro-Channel Cooling Using Finite Element Analysis
Abstract: Due to the enormous heat fluxes emitted by modern electronic chips, there is a persistent need to enhance the efficiency of cooling systems. This study's focus is on optimizing heat transfer in micro-channel heat sinks that use liquid cooling. Geometric changes and the use of nano-fluids as coolants in place of water are performed to achieve this goal with little energy consumption. Numerical analysis of pipe micro-channel fluid flow and …
Published in International Journal of Energy and Thermal Applications · Vol. 1, Issue 1, 2023 · pp. 36–44 Read article
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Effects of Bearing Design Parameter on Working Characteristics of Floating Ring Bearing
Abstract: The working stability of turbochargers supported by floating ring bearings depends on not only the structure of the rotors but also working characteristic of floating ring bearings. These working characteristics are related to working conditions and design parameters of floating ring bearings. The main goal of this research is to investigate the working characteristics of bearings by design parameters of floating ring bearings. In order to study the working characteristics …
Published in Journal of Experimental & Applied Mechanics · Vol. 15, Issue 3, 2024 · pp. 39–52 Read article